Bayesian and non-Bayesian reliability estimation of multicomponent stress–strength model for unit Weibull distribution

Abstract

Mazucheli et al. introduced a new transformed model referred as the unit-Weibull (UW) distribution with uni-and anti-unimodal, decreasing and increasing shaped density along with bathtub shaped, constant and non-decreasing hazard rates. Here we consider inference upon stress and strength reliability using different statistical procedures. Under the framework that stress-strength components follow UW distributions with a known shape, we first estimate multicomponent system reliability by using four different frequentist methods. Besides, asymptotic confidence intervals (CIs) and two bootstrap CIs are obtained. Inference results for the reliability are further derived from Bayesian context when shape parameter is known or unknown. Unbiased estimation has also been considered when common shape is known. Numerical comparisons are presented using Monte Carlo simulations and in consequence, an illustrative discussion is provided. Two numerical examples are also presented in support of this study. Significant conclusion: We have investigated inference upon a stress-strength parameter for UW distribution. The four frequentist methods of estimation along with Bayesian procedures have been used to estimate the system reliability with common parameter being known or unknown.

Statistical inference for multi stress–strength reliability based on progressive first failure with lifetime inverse Lomax distribution and analysis of transformer insulation data

“…Despite the fact that Bhattacharyya and Johnson 16 developed the multicomponent stress-strength model, it has garnered a lot of attention in recent years and has been explored by numerous researchers for both complete and censored data. Some of the recently appeared articles include Tolba et al, 17 Ramadan et al, 18 Kotb and Raqab, 19 Maurya and Tripathi, 20 Mahto et al, 21 Wang et al, 22 Jha et al, 23 El-Sagheer et al, 24 Rasekhi et al, 25 Alotaibi et al, 26 Maurya et al, 27 Sarhan et al, 28 Sarhan et al, 29 Kohansal and Shoaee, 30 Muse et al, 31 Jana and Bera, 32 Ahmad et al, 33 Ahmad et al 34 , Ramadan 35 and Wu and Kuş. 36 Well-known censoring techniques include the type-II censoring scheme, progressive type-II censoring scheme, and progressive first failure censoring system.…”

Optimal Plan of Multi-Stress–Strength Reliability Bayesian and Non-Bayesian Methods for the Alpha Power Exponential Model Using Progressive First Failure

“…Despite the fact that Ref. [12] developed the multi-component stress-strength model decades ago, it has garnered a lot of attention in recent years and has been explored by numerous scholars for both complete and filtered data [13][14][15][16][17]. Stress-strength reliability, R = P(X < Y), has been extensively investigated as a stress-strength model, and the research has also been extended to multi-component systems.…”

Multicomponent stress-strength reliability estimation based on unit generalized Rayleigh distribution

“…Proposed estimates are compared using Monte Carlo simulations and discussions are presented. Further Alotaibi et al (2020) considered estimation for stress-strength reliability using different methods when components of system follow unit distributions with a common shape parameter. Different estimation methods are applied to estimate the reliability.…”